60.2.243 problem 819

Internal problem ID [10830]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 819
Date solved : Tuesday, January 28, 2025 at 05:20:37 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {2 x}{3}+\sqrt {x^{2}+3 y}+x^{2} \sqrt {x^{2}+3 y}+x^{3} \sqrt {x^{2}+3 y} \end{align*}

✓ Solution by Maple

Time used: 0.312 (sec). Leaf size: 30

dsolve(diff(y(x),x) = -2/3*x+(x^2+3*y(x))^(1/2)+x^2*(x^2+3*y(x))^(1/2)+x^3*(x^2+3*y(x))^(1/2),y(x), singsol=all)
 

\[ c_{1} +\frac {3 x^{4}}{8}+\frac {x^{3}}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y} = 0 \]

✓ Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 63

DSolve[D[y[x],x] == (-2*x)/3 + Sqrt[x^2 + 3*y[x]] + x^2*Sqrt[x^2 + 3*y[x]] + x^3*Sqrt[x^2 + 3*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{192} \left (9 x^8+24 x^7+16 x^6+72 x^5+(96-72 c_1) x^4-96 c_1 x^3+80 x^2-288 c_1 x+144 c_1{}^2\right ) \]